Answer to Question #2107 in Calculus for Abhilash

Question

Suppose that the cost (in dollars) for a company to produce x pairs of a new line of jeans is described by the formula below.
C(x) = 2500 + 4x + 0.02x2 + 0.0002x3

.

(b) Find C'(140).

Answer 1

<img src="/cgi-bin/mimetex.cgi?C%27%28x%29%20=%204%20+%200.02%20%5Ccdot%202x%20+%200.0002%20%5Ccdot%203x%5E2%20=%204+%200.04x+0.0006x%5E2%20%5C%5C%20C%27%28140%29%20=%204%20+%200.04*140%20+%200.0006*140%5E2%20=%2021.36" title="C'(x) = 4 + 0.02 \cdot 2x + 0.0002 \cdot 3x^2 = 4+ 0.04x+0.0006x^2 \\ C'(140) = 4 + 0.04*140 + 0.0006*140^2 = 21.36">